Physics study notes
Physics for the NMAT: Mechanics, Energy, Waves, Electricity, and Thermodynamics
Key points
- Kinematics equations (v = u + at, s = ut + (1/2)at^2, v^2 = u^2 + 2as) apply only under constant acceleration.
- Newton's second law, F = ma, is the central tool for analyzing forces; always start with a free-body diagram.
- The work-energy theorem links net work to the change in kinetic energy; mechanical energy is conserved only without friction or other energy losses.
- Momentum (p = mv) is always conserved in collisions; kinetic energy is conserved only in elastic collisions.
- Torque (τ = rF sinθ) and moment of inertia (I) are the rotational analogs of force and mass; τ = Iα is the rotational form of Newton's second law.
- Wave speed follows v = fλ; constructive interference occurs at path differences of whole wavelengths, destructive at half-wavelength offsets.
- Snell's law (n1 sinθ1 = n2 sinθ2) governs refraction; total internal reflection occurs beyond the critical angle when light moves to a less dense medium.
- The thin lens equation (1/f = 1/d_o + 1/d_i) predicts image location; converging lenses form real or virtual images depending on object placement relative to the focal point.
- Ohm's law (V = IR) and the rules for series (resistances add) versus parallel (reciprocals add) circuits are essential for circuit analysis.
- Faraday's law (EMF = ΔΦ/Δt) and Lenz's law explain electromagnetic induction, the basis of generators and transformers.
- Specific heat (Q = mcΔT) and latent heat (Q = mL) calculate heat needed for temperature change and phase change, respectively.
- The first law of thermodynamics (ΔU = Q − W) and Carnot efficiency (e = 1 − Tc/Th) describe energy conservation and the limits of heat engines.
Kinematics and Newton's Laws
Kinematics describes motion using displacement, velocity, and acceleration without regard to its cause. For constant acceleration, four equations connect these quantities: v = u + at, s = ut + (1/2)at^2, v^2 = u^2 + 2as, and s = ((u+v)/2)t, where u is initial velocity, v is final velocity, a is acceleration, t is time, and s is displacement. Newton's three laws of motion explain why objects move as they do. The first law (inertia) states an object remains at rest or in uniform motion unless acted on by a net external force. The second law quantifies this: net force equals mass times acceleration (F = ma). The third law states that for every action force, there is an equal and opposite reaction force. On the NMAT, expect problems requiring free-body diagrams that identify gravity, normal force, tension, friction, and applied forces, then apply F = ma along relevant axes. Projectile motion combines constant horizontal velocity with constant vertical acceleration due to gravity, and circular motion requires a centripetal force (Fc = mv^2/r) directed toward the center of the circular path.
Work, Energy, and Power
Work is done when a force causes displacement: W = Fd cos(θ), where θ is the angle between the force and displacement directions. The work-energy theorem states that the net work done on an object equals its change in kinetic energy. Kinetic energy is KE = (1/2)mv^2, and gravitational potential energy near Earth's surface is PE = mgh, measured relative to a chosen reference height. In an isolated system without friction, total mechanical energy (KE + PE) is conserved; in real systems, some energy is dissipated as heat due to friction or air resistance, and this lost energy can be calculated by comparing initial and final mechanical energy. Power is the rate of doing work: P = W/t, or equivalently P = Fv for a force acting on a moving object. Elastic potential energy stored in an ideal spring follows Hooke's law: PE_spring = (1/2)kx^2, where k is the spring constant and x is displacement from natural length. Collisions are classified as elastic (kinetic energy conserved) or inelastic (kinetic energy not conserved, though momentum always is), and NMAT problems often ask you to compute velocities after collision or the fraction of energy lost.
Momentum, Collisions, and Rotational Motion
Momentum (p = mv) is conserved in any closed system with no external net force, making it the key tool for analyzing collisions. In a perfectly inelastic collision, objects stick together and move with a common final velocity found from total momentum divided by total mass. In an elastic collision, both momentum and kinetic energy are conserved, allowing both final velocities to be solved using standard formulas; a useful special case is that when a moving object strikes a stationary object of equal mass elastically, their velocities are simply exchanged. Impulse (J = FΔt = Δp) links force, time, and momentum change, explaining why extending contact time (like padding or airbags) reduces peak force. Rotational motion parallels linear motion: torque (τ = rF sinθ) is the rotational analog of force, and moment of inertia (I) is the rotational analog of mass, varying by shape (for example, I = (1/2)MR^2 for a uniform solid disk about its central axis). Newton's second law becomes τ = Iα, connecting net torque to angular acceleration, and objects in rotational equilibrium have balanced torques, as in seesaw or lever problems.
Waves, Sound, and the Doppler Effect
A wave transfers energy through a medium without net transfer of matter. Key wave properties include wavelength (λ), frequency (f), period (T = 1/f), and amplitude, related by the universal wave equation v = fλ. Transverse waves (like light and waves on a string) oscillate perpendicular to the direction of travel, while longitudinal waves (like sound) oscillate parallel to it. When two or more waves overlap, they superpose: constructive interference occurs when path differences are whole-number multiples of the wavelength, producing reinforced amplitude, while destructive interference occurs at half-wavelength offsets, reducing or canceling amplitude. Standing waves form when waves reflect back on themselves in a bounded medium, such as a string fixed at both ends or a resonating air column in a pipe; the allowed wavelengths depend on the boundary conditions (open or closed ends) and determine the harmonic series a system can produce. The Doppler effect describes the apparent shift in frequency when a source and observer are in relative motion: frequency appears higher when they approach each other and lower when they move apart, a principle used in radar, medical ultrasound, and astronomy.
Geometric Optics: Reflection, Refraction, and Lenses
Light traveling between media of different refractive indices bends according to Snell's law: n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are angles measured from the normal to the surface. Reflection occurs when light bounces off a surface, with the angle of incidence equal to the angle of reflection. When light travels from a denser to a less dense medium at an angle beyond the critical angle (where sinθc = n2/n1), total internal reflection occurs, and no light escapes into the second medium; this principle underlies fiber optics. Lenses form images according to the thin lens equation, 1/f = 1/d_o + 1/d_i, where f is focal length, d_o is object distance, and d_i is image distance. Converging (convex) lenses can form real, inverted images when the object is beyond the focal length, or virtual, upright, magnified images when the object is within the focal length (as in a magnifying glass). Diverging (concave) lenses always form virtual, upright, reduced images. Magnification is given by m = -d_i/d_o, with the sign indicating orientation.
Electric Charge, Fields, and Circuits
Electric charge interactions follow Coulomb's law: F = kq1q2/r^2, where k ≈ 9×10^9 N·m^2/C^2. This force creates an electric field, E = F/q, pointing away from positive charges and toward negative charges. Electric potential difference (voltage) represents energy per unit charge, and current is the rate of charge flow: I = Q/t. Ohm's law, V = IR, relates voltage, current, and resistance for many conductive materials. In series circuits, current is the same everywhere and resistances add directly; in parallel circuits, voltage is the same across each branch and the reciprocal of the equivalent resistance equals the sum of the reciprocals of each branch's resistance. Power dissipated in a resistor can be calculated three equivalent ways: P = IV, P = I^2R, or P = V^2/R. Capacitors store electric energy, U = (1/2)CV^2, and in an RC circuit, the time constant τ = RC characterizes the charging or discharging rate, with about 63% of maximum charge reached after one time constant.
Magnetism and Electromagnetic Induction
Moving electric charges create magnetic fields, and magnetic fields exert forces on moving charges and current-carrying conductors. The force on a straight current-carrying wire in a uniform magnetic field is F = BIL sinθ, where B is magnetic field strength, I is current, L is the wire's length within the field, and θ is the angle between the wire and the field. Faraday's law of electromagnetic induction states that a changing magnetic flux through a loop induces an electromotive force (EMF): EMF = ΔΦ/Δt, where Φ = BA cosθ is magnetic flux. Lenz's law adds that the induced current always flows in a direction that opposes the change in flux that caused it, a manifestation of energy conservation. These principles underlie electric generators (mechanical energy converts to electrical energy via changing flux) and transformers, which use changing magnetic flux in a primary coil to induce a voltage in a secondary coil; the voltage ratio equals the turns ratio, Vs/Vp = Ns/Np, while real transformers lose some power to resistance and heat, reducing overall efficiency below 100%.
Heat, Temperature, and the Laws of Thermodynamics
Temperature measures the average kinetic energy of particles in a substance, while heat is the energy transferred between systems due to a temperature difference. The Celsius and Kelvin scales are related by K = °C + 273, with absolute zero (0 K) representing the theoretical minimum temperature. Specific heat capacity relates heat added to temperature change: Q = mcΔT. When substances change phase (melting, freezing, boiling, condensing) at constant temperature, the heat involved is calculated using latent heat: Q = mL, where L is the latent heat of fusion or vaporization specific to the substance. Heat transfers by conduction (through direct particle contact, faster in materials with higher thermal conductivity), convection (through bulk fluid movement), and radiation (through electromagnetic waves, requiring no medium). The first law of thermodynamics, ΔU = Q − W, states that a system's internal energy change equals heat added minus work done by the system. The second law introduces entropy, establishing that heat spontaneously flows from hot to cold and that no engine can be perfectly efficient; the theoretical maximum (Carnot) efficiency between two reservoirs is e = 1 − (Tc/Th), using absolute temperatures.
Ideal Gases and Problem-Solving Strategy
The ideal gas law, PV = nRT, connects pressure (P), volume (V), number of moles (n), the gas constant (R), and absolute temperature (T) for a gas that behaves ideally. When comparing two states of the same fixed amount of gas, the combined gas law, P1V1/T1 = P2V2/T2, is often more convenient, since it eliminates the need to know n or R explicitly. For NMAT physics problems generally, a consistent strategy helps: identify the given quantities and what is being asked, choose the relevant equation(s) linking those quantities, watch for consistent units (especially converting Celsius to Kelvin for gas law problems, or grams to kilograms for mechanics), and check whether the final answer is physically reasonable in magnitude and direction. Many multi-step problems combine two or more concepts, such as kinematics with Newton's laws, or energy conservation with friction losses, so identifying every force or energy transfer at play before calculating is essential to avoiding careless errors.
References
- OpenStax University Physics Volume 1 — OpenStax
- OpenStax University Physics Volume 2 — OpenStax
- Khan Academy: One-Dimensional Motion — Khan Academy
- Khan Academy: Work and Energy — Khan Academy
- Khan Academy: Mechanical Waves and Sound — Khan Academy
- Khan Academy: Circuits — Khan Academy
- Khan Academy: Thermodynamics — Khan Academy
- LibreTexts: Classical Mechanics — LibreTexts
Ready to practice?
Put these physics concepts to the test with practice questions.